Abel变换数值反演的离散正则化方法

基于Tikhonov的正则化思想,将Abel变换的理论反演公式与对数值求导的离散正则化处理以及带权的Gauss型积分相结合,给出了Abel变换数值反演的一个新算法,并进行了理论分析与数值实验。结果表明:该算法具有精度高、数值稳定等优点。     

将噪声作为独立变量的动态光散射数据反演

在动态光散射颗粒测量时,为了从含噪的自相关函数数据中准确地反演出颗粒粒度分布,对Tikhonov正则化算法进行改进,将噪声作为一个独立的未知变量应用到正则化方程中进行粒度反演.在计算过程中,相应增加方程中各系数矩阵的行数和列数,对求解的粒度分布数值则仍取其原来方程的行数和列数,从而达到对部分噪声的剔除作用.不同噪声水平下的颗粒粒度反演结果表明,改进后的算法能够显著提高低信噪比动态光散射数据粒度反演结果的准确性,适用于宽分布较大粒径的颗粒粒度反演.     

将噪声作为独立变量的动态光散射数据反演（英文）

在动态光散射颗粒测量时,为了从含噪的自相关函数数据中准确地反演出颗粒粒度分布,对Tikhonov正则化算法进行改进,将噪声作为一个独立的未知变量应用到正则化方程中进行粒度反演.在计算过程中,相应增加方程中各系数矩阵的行数和列数,对求解的粒度分布数值则仍取其原来方程的行数和列数,从而达到对部分噪声的剔除作用.不同噪声水平下的颗粒粒度反演结果表明,改进后的算法能够显著提高低信噪比动态光散射数据粒度反演结果的准确性,适用于宽分布较大粒径的颗粒粒度反演.     

中子深度分析反演算法研究

针对中子深度分析技术,研究几类反演算法：概率迭代法、奇异值分解求解最小二乘法、线性正则化方法及约束线性正则化法.开展相关数值实验,分别在欠定方程、超定方程情况下,对反演算法的结果进行比较.一般情况下几种算法都能得到较为理想的结果,概率迭代法和约束线性正则化法由于有迭代过程,因此在离子源强度发生阶跃处得到的结果并不理想.在超定方程情况下,当选取的反演范围较为随意时,线性正则化方法可能使得解的稳定性较差,而约束线性正则化法能够很好地抑制求解过程中的不稳定性.对实际测量能谱进行反演时,由于能谱有随机误差,线性正则化方法不能很好地抑制误差的影响,反演结果振荡较强,其余方法的结果与参考值符合很好.     

垂直天线阵观测信息反演大气折射率廓线

利用垂直天线阵观测得到的电磁场信息建立目标泛函,从电磁波抛物方程传播模式出发,利用偏微分方程最优控制中的伴随方法研究大气折射率廓线反演问题. 针对反演的不适定性,采用正则化思想对目标泛函进行改造,并根据变分同化思想构建反演迭代格式. 数值模拟试验验证了理论算法的可行性. 由于采用分步Fourier算法求解电磁波抛物方程传播模式和伴随模式过程中产生的固有误差随着传播距离的增加累积增大,反演廓线在传播距离较远时不能收敛于观测廓线. 在这种情况下,引入较好的初猜廓线和背景场可以有效地改进反演结果. 关键词： 大气折射率 电磁波抛物方程 变分伴随 正则化     

用进化策略方法反演二维弹性波动方程的参数

从材料响应的理论合成与实际测量数据相拟合出发,将二维弹性波动方程的参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了进化策略法,并同遗传方法的反演结果进行了比较.数值结果表明,用进化策略方法进行参数反演的精度大大高于用遗传方法进行参数反演的精度,进化策略反演是一种良好的非线性反演方法.     

合成孔径雷达图像反演海面风向新方法的研究

提出了利用基于Tikhonov正则化的二维数值微分方法来反演合成孔径雷达图像海面风向的新方法. 首先将高分辨率合成孔径雷达图像去噪、降采样并分割成数个子图像,利用基于Tikhonov正则化的二维数值微分方法求解所关注子图像每一个点的梯度方向,在此基础上通过带有距离权重的目标函数确定子图像整体强度的梯度方向,该梯度的垂线方向就是所要求解的风向,然后进行模拟试验,在添加误差为10%的随机扰动情况下,分别基于Tikhonov正则化的二维数值微分方法与基于有限差分的Sobel算子方法来反演风向,结果表明,前者误差为0.7293°,后者误差为13.5069°,最后进行了实例试验,结果显示,Sobel算子方法的部分风向反演结果偏离整体风向明显,而基于Tikhonov正则化的二维数值微分方法的风向反演结果一致性较好. 将三个船舶报风向与相应位置合成孔径雷达图像的海面风向反演结果进行对比,Sobel算子方法的风向反演结果平均误差在9.0331°,而基于Tikhonov正则化的二维数值微分方法的风向反演结果平均误差仅为1.1148°. 关键词： 合成孔径雷达 海面风向 数值微分 Sobel算子     

大气廓线参数反演中基于大气可反演指数的正 则化参数选择方法

以大气可反演指数为指标, 采用Nelder-Mead单纯形法求解方法, 提出了一种卫星遥感资料反演大气廓线算法中动态的正则化参数选择方案. 同时针对四条典型区域廓线, 进行了选择试验. 从选择结果看, 不同廓线所对应的最优正则化参数变化幅度非常小, 因此在实际反演过程中, 为提高计算效率, 可近似取正则化参数为固定值. 这为利用卫星遥感资料进行大气廓线反演问题中正则化参数的选择提供了一种可借鉴的方法.     

基于优化理论的高频地波雷达海浪参数反演

针对从高频地波雷达海洋回波多普勒谱反演海浪参数的非线性积分方程,采用线性化近似可以转化为线性积分方程,类似于第一类Fredholm积分方程.文中采用数值方法将线性积分方程转化为二次型最优化问题,并采用共轭梯度法来求解.针对海浪参数的非负先验特性,在迭代过程中,加入非负约束项对共轭梯度法进行了改进.在单部雷达和双部雷达情况下进行正演数值模拟,然后用模拟数据添加不同信噪比的随机噪声进行海浪参数反演,无论是单峰海浪谱还是有两个传播方向的双峰谱反演结果均表明了本文提出的算法在不同信噪比下的有效性.     

二维波动方程数值反演的迭代方法

本文针对二维波动方程的反演问题，提出了一种新的迭代方法。该方法是一种牛顿型迭代，并且每步迭代都利用吉洪诺夫正则化方法克服反问题的不适定性，因此具有良好的数值稳定性。文中给出了数值仿真实例说明了本方法的可行性及有效性。     

一种求解逆风下火焰沿柱状燃料传播的数值方法

1引言近十几年来，国内外许多人对火焰沿薄燃料层的传播进行了研究，但很少涉及到火焰沿柱状燃料的传播。图1为所研究问题的物理模型。火焰的传播涉及到气固两相的相互作用，两相界面上存在能量和质量的交换，气相中存在着气气间的化学反应，固相中存在着裂解反应。当参考坐标系团结在火焰前锋上时，该火焰传播问题成为一准稳态问题，燃料以一固定速度供给火焰。2数学模型2．1守恒方程气相的所有守恒方程均服从下列通用方程：其中、，L和一分别表示通用变量、广义扩散系数和广义源项。固相包括：质量守恒方程：。。能量守恒方程：2．2边界…     

Efficient spectral and pseudospectral algorithms for 3D simulations of whistler-mode waves in a plasma

Efficient spectral and pseudospectral algorithms for simulation of linear and nonlinear 3D whistler waves in a cold electron plasma are developed. These algorithms are applied to the simulation of whistler waves generated by loop antennas and spheromak-like stationary waves of considerable amplitude. The algorithms are linearly stable and show good stability properties for computations of nonlinear waves over tens of thousands of time steps. Additional speedups by factors of 10–20 (comparing single core CPU and one GPU) are achieved by using graphics processors (GPUs), which enable efficient numerical simulation of the wave propagation on relatively high resolution meshes (tens of millions nodes) in personal computing environment. Comparisons of the numerical results with analytical solutions and experiments show good agreement. The limitations of the codes and the performance of the GPU computing are discussed.     

A class of Cartesian grid embedded boundary algorithms for incompressible flow with time-varying complex geometries

We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional direct-forcing immersed boundary methods: the proposed algorithms calculate and apply the force density in the extended solid domain to uphold the solid velocity and hence the boundary condition at the rigid-body surface. The principle of the embedded boundary algorithm allows us to solve the fluid equations on a Cartesian grid with a set of external forces spread onto the grid points occupied by the rigid structure. The proposed algorithms use the MAC (marker and cell) algorithm to solve the incompressible Navier-Stokes equations. Unlike projection methods, the MAC scheme incorporates the gradient of the force density in solving the pressure Poisson equation, so that the dipole force, due to the jump of pressure across the solid-fluid interface, is directly balanced by the gradient of the force density. We validate the proposed algorithms via the classical benchmark problem of flow past a cylinder. Our numerical experiments show that numerical solutions of the velocity field obtained by using the proposed algorithms are smooth across the solid-fluid interface. Finally, we consider the problem of a cylinder moving between two parallel plane walls. Numerical solutions of this problem obtained by using the proposed algorithms are compared with the classical asymptotic solutions. We show that the two solutions are in good agreement.     

两种TVD格式在跨音透平叶栅流场计算中的应用

两种ＴＶＤ格式在跨音透平叶栅流场计算中的应用黄伟光，刘建军（中国科学院工程热物理研究所北京１０００８０）关键词跨音速透平，Ｅｕｌｅｒ方程，ＴＶＤ格式１引言现代高负荷透平大都工作在跨音范围，研究发展能准确预测跨音速透平叶栅内部流场的激波位置与强度以及叶...     

Numerical model reduction of 2D steady incompressible laminar flows: Application on the flow over a backward-facing step

The numerical solution of most fluid mechanics problems usually needs such a fine mesh that the associated computational times become non-negligible parts in any design process. In order to couple numerical modelling schemes with inversion or control algorithms, the size of such models needs to be highly reduced. The identification method is a way to build low-order models that fit with the original ones. The laminar flow over a backward-facing step is used as a test case. Presented solutions are found to be in good agreement with experimental and numerical results found in the literature.     

关于分区模拟无粘流内边界守恒算法的相容性

本文讨论用分区方法计算可压缩无粘流动的内边界通量守恒算法。分析指出插值型通量守恒算法不保证相容性条件,计算表明这种不相容性能引起数值解出现明显误差,或破坏其稳定性、收敛性。为此,文中提出内边界采用自适应算法并给出了算例。     

CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION

With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.^[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.^[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified.     

等离子体的能量分布和电位的数值计算

在方磁阱近似、各向同性位近似以及最低模近似下,用数值方法求解了简化的F-P方程。得到了若干数值结果,结果与物理分析相符合。同时,本文详细地叙述了数值方法。     

求解隐式差分方程的并行算法

本文研究了求解隐式差分方程的并行算法,其基本想法是把差分方程组化为若干个子方程组来求解,文中给出了直接法和迭代法,证明了迭代法的收敛性。为了说明分段隐式迭代方法的有效性,文中针对扩散方程的具体例子给出了数值试验计算结果。     

A New Two-Stage Algorithm for Solving Optimization Problems

Optimization seeks to find inputs for an objective function that result in a maximum or minimum. Optimization methods are divided into exact and approximate (algorithms). Several optimization algorithms imitate natural phenomena, laws of physics, and behavior of living organisms. Optimization based on algorithms is the challenge that underlies machine learning, from logistic regression to training neural networks for artificial intelligence. In this paper, a new algorithm called two-stage optimization (TSO) is proposed. The TSO algorithm updates population members in two steps at each iteration. For this purpose, a group of good population members is selected and then two members of this group are randomly used to update the position of each of them. This update is based on the first selected good member at the first stage, and on the second selected good member at the second stage. We describe the stages of the TSO algorithm and model them mathematically. Performance of the TSO algorithm is evaluated for twenty-three standard objective functions. In order to compare the optimization results of the TSO algorithm, eight other competing algorithms are considered, including genetic, gravitational search, grey wolf, marine predators, particle swarm, teaching-learning-based, tunicate swarm, and whale approaches. The numerical results show that the new algorithm is superior and more competitive in solving optimization problems when compared with other algorithms.